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Binary Decomposition: A Problem Transformation Perspective for Open-Set Semi-Supervised Learning
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Proposes BDMatch, which turns open-set semi-supervised learning into K standard binary SSL problems (one-vs-all) and addresses the resulting class imbalance with adaptive logit adjustment and representation compromise with label-specific attention features.
Problem
Open-set semi-supervised learning, where unlabeled data contains outliers from novel categories absent from labeled data; existing detect-and-filter methods suffer from error-prone outlier detection.
Approach
Binary decomposition transforms the open-set SSL problem into K one-vs-all binary SSL problems so outliers become negatives and no outlier detection is needed; adaptive logit adjustment uses running prediction averages as a proxy for unlabeled class imbalance, and per-class dot-product attention gives label-specific features.
Key results
- BDMatch achieves 91.77% inlier accuracy on CIFAR-10 with 6 seen classes and 4 labels per class, versus 89.68% for the second best (IOMatch).
- On CIFAR-100-80-25 and ImageNet-30-20-p1, BDMatch improves the existing best overall accuracy by 12.21% and 13.46% respectively.
- Ablations show removing label-specific features drops CIFAR-100-20-4 inlier accuracy from 58.05 to 54.45, and removing the adaptive proxy drops it to 54.50.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use binary decomposition with BDMatch instead of the strongest reported baseline | Open-set SSL · CIFAR-10, CIFAR-100, and ImageNet-30 settings in Tables 1–2 | inlier and overall accuracy: 91.77±1.62 vs 89.68±2.04 (CIFAR-10 inlier, 4 labels/class); 78.31±0.89 vs 66.32±3.67 (CIFAR-10 overall, 4 labels/class) | Helped |
| add outliers to training instead of using purified data (ablation) | BDMatch · CIFAR-100 (20/80, 4 labels/class) | inlier accuracy: 54.75 -> 58.05 | Helped |
| add outliers to training instead of using purified data (ablation) | BDMatch · CIFAR-100 (80/20, 4 labels/class) | inlier accuracy: 52.36 -> 53.83 | Helped |
| add label-specific features (ablation) | BDMatch · CIFAR-100 (20/80, 4 labels/class) | inlier accuracy: 54.45 -> 58.05 | Helped |
| add label-specific features (ablation) | BDMatch · CIFAR-100 (80/20, 4 labels/class) | inlier accuracy: 51.24 -> 53.83 | Helped |
| add dual-branch architecture (ablation) | BDMatch · CIFAR-100 (20/80, 4 labels/class) | inlier accuracy: 55.85 -> 58.05 | Helped |
| add dual-branch architecture (ablation) | BDMatch · CIFAR-100 (80/20, 4 labels/class) | inlier accuracy: 52.19 -> 53.83 | Helped |
| use an adaptive proxy for logit adjustment instead of labeled-set imbalance ratio (ablation) | BDMatch · CIFAR-100 (20/80, 4 labels/class) | inlier accuracy: 54.50 -> 58.05 | Helped |
| use an adaptive proxy for logit adjustment instead of labeled-set imbalance ratio (ablation) | BDMatch · CIFAR-100 (80/20, 4 labels/class) | inlier accuracy: 49.28 -> 53.83 | Helped |
| add non-adaptive logit adjustment (ablation) | BDMatch · CIFAR-100 (20/80, 4 labels/class) | inlier accuracy: 52.55 -> 58.05 | Helped |
| add non-adaptive logit adjustment (ablation) | BDMatch · CIFAR-100 (80/20, 4 labels/class) | inlier accuracy: 43.86 -> 53.83 | Helped |
| add re-margining to the supervised loss (ablation) | BDMatch · CIFAR-100 (20/80, 4 labels/class) | inlier accuracy: 55.70 -> 58.05 | Helped |
Surprising findings
- Training on an oracle-purified inlier-only set performs worse than BDMatch using the full unlabeled set including outliers, suggesting outliers are useful under binary decomposition.
Limitations
- Parameter sensitivity: the scaling parameter tau must be tuned, with both under- and over-balancing harmful.
- Label-specific feature implementation is given for image data only; text and tabular variants are deferred to the appendix.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 ImageNet-30 SVHN LSUN Synthetic Gaussian Synthetic Uniform
Benchmarks: CIFAR-10 CIFAR-100 ImageNet-30
Metrics: inlier accuracy balanced accuracy (overall accuracy)
Baselines: MixMatch ReMixMatch FixMatch CoMatch FlexMatch SimMatch FreeMatch UASD DS3L MTCF T2T OpenMatch
Builds on: FixMatch USB logit adjustment re-margining loss
Closest papers by meaning
- OpenMatch: Open-Set Semi-supervised Learning with Open-set Consistency Regularization (NeurIPS 2021 · similarity 0.90)
- Don’t fear the unlabelled: safe semi-supervised learning via debiasing (ICLR 2023 · similarity 0.87)
- On Non-Random Missing Labels in Semi-Supervised Learning (ICLR 2022 · similarity 0.87)
- CGMatch: A Different Perspective of Semi-supervised Learning (CVPR 2025 · similarity 0.86)
- Erasing the Bias: Fine-Tuning Foundation Models for Semi-Supervised Learning (ICML 2024 · similarity 0.85)
- Unknown-Aware Graph Regularization for Robust Semi-supervised Learning from Uncurated Data (AAAI 2024 · similarity 0.85)
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